CN113259107B - Grid-based dual-mode encryption method - Google Patents

Grid-based dual-mode encryption method Download PDF

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CN113259107B
CN113259107B CN202110692785.3A CN202110692785A CN113259107B CN 113259107 B CN113259107 B CN 113259107B CN 202110692785 A CN202110692785 A CN 202110692785A CN 113259107 B CN113259107 B CN 113259107B
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bit
mode
public key
plaintext
key
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CN113259107A (en
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刘沫萌
王珍珍
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Xian Polytechnic University
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
    • H04L9/30—Public key, i.e. encryption algorithm being computationally infeasible to invert or user's encryption keys not requiring secrecy
    • H04L9/3006—Public key, i.e. encryption algorithm being computationally infeasible to invert or user's encryption keys not requiring secrecy underlying computational problems or public-key parameters
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F21/00—Security arrangements for protecting computers, components thereof, programs or data against unauthorised activity
    • G06F21/60—Protecting data
    • G06F21/602—Providing cryptographic facilities or services
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L63/00—Network architectures or network communication protocols for network security
    • H04L63/04—Network architectures or network communication protocols for network security for providing a confidential data exchange among entities communicating through data packet networks
    • H04L63/0428—Network architectures or network communication protocols for network security for providing a confidential data exchange among entities communicating through data packet networks wherein the data content is protected, e.g. by encrypting or encapsulating the payload
    • H04L63/0442—Network architectures or network communication protocols for network security for providing a confidential data exchange among entities communicating through data packet networks wherein the data content is protected, e.g. by encrypting or encapsulating the payload wherein the sending and receiving network entities apply asymmetric encryption, i.e. different keys for encryption and decryption
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
    • H04L9/08—Key distribution or management, e.g. generation, sharing or updating, of cryptographic keys or passwords
    • H04L9/0861—Generation of secret information including derivation or calculation of cryptographic keys or passwords
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L2209/00—Additional information or applications relating to cryptographic mechanisms or cryptographic arrangements for secret or secure communication H04L9/00
    • H04L2209/50—Oblivious transfer

Abstract

The invention discloses a lattice-based dual-mode encryption method, which specifically comprises the following steps: firstly, generating a common reference string crs by using a Setup algorithm in a Messy mode or a Decryption mode; secondly, selecting parameters, Bob generates a public key pk by using a secret key generation algorithm0And the private key skb(ii) a Alice encrypts the multi-bit plaintext message by using an encryption algorithm and generates a ciphertext; and finally, Bob decrypts the multi-bit plaintext message by using a decryption algorithm and recovers the plaintext message. The method of the invention solves the defect that the existing dual-mode encryption method on the lattice can only encrypt single-bit messages, provides a more efficient dual-mode encryption method, and can encrypt and transmit multi-bit messages on the basis of keeping the derived OT protocol capable of keeping UC security. The invention makes the dual-mode encryption method more efficient and can be used in a secure multi-party computing scenario.

Description

Grid-based dual-mode encryption method
Technical Field
The invention belongs to the technical field of information security, and particularly relates to a dual-mode encryption method based on lattices.
Background
The public key cryptography can provide key technical theory support such as encryption, authentication, security protocol and the like for the fields of network and information security due to the powerful cryptographic service function. The breakthrough progress of quantum computing technology forms fatal threats to a large number decomposition type and discrete logarithm type public key cryptosystem, so that the 'post-quantum cryptosystem' attracts extensive attention and research in the industry, wherein the 'lattice public key cryptosystem' is represented by the most concerned class in the field by the unique comprehensive advantages (quantum attack resistance, reduction characteristic from the worst case to the average case, simple algorithm, low asymptotic complexity and rich cryptographic service functions).
As a basic two-party computing cryptographic primitive, an Oblivious Transfer (OT) is often applied to a basic operation module in a secure multiparty computing implementation protocol in a black box form. In addition, many cryptographic tasks can be reduced to utilizing the OT to implement their particular functional functions. OT is defined as the sender (marked S) and receiver (marked R) being each a pair of messages (μ;)0,μ1) And a message selection bit b e {0,1} as respective inputs, requiring that R can only receive a message mu selected by itselfbFor another message mu1-bCannot be known; s then the message option b of R cannot be known. Many of the OT protocol schemes currently proposed are either only capableThe security of half-simulation (half-simulation) is obtained, and the half-simulation cannot be integrated into a multi-party computing scene for combined use with other protocols; or, the security of 'full-simulation' is obtained under 'stand-alone model', only the protocol is allowed to be continuously combined with other protocols for use, and the requirement that the cryptographic protocol needs to be asynchronously combined and executed in the modern computer network cannot be met. Therefore, it becomes an important index for designing OT protocol to obtain security under the "Universal Combination (UC)" model (fully-emulated security model that allows arbitrary combinations between protocols to be used).
In 2008, Peikert et al proposed a dual-mode encryption framework (dual-mode encryption framework) under the Common Reference String (CRS) model, and can derive the UC-safe OT protocol and instantiate it With the difficult problem of error Learning (LWE). However, the security of this lattice instantiation scheme in the Decryption mode is weakened, resulting in that the receiver of the OT protocol only obtains computational security (computational security), and CRS can only be used a limited number of times, greatly affecting the protocol performance. In 2020, Quach uses noise flooding (noise flooding) technique to upgrade the receiver security of the above lattice dual mode encryption scheme in Decryption mode to statistical security (statistical security). However, the cost of exploiting noise flooding is the use of a super polynomial modulus, resulting in an inability to construct an efficient emulator for malicious recipients in the UC security attestation of the OT protocol. To solve this problem, Quach utilizes an integer function that approximates an Approximate Smooth Projection Hash (ASPH) function on the middle lattice, making the simulator construction independent of modulus selection. However, the rounding function can only output a 1-bit hash value to conceal a plaintext message in a dual-mode encryption system, and can only achieve the goal by an OT protocol that independently repeats a single-bit message transmission multiple times, if the hidden multi-bit message transmission requirement is to be met. It can be seen that the goodness of the OT protocol design depends on the performance of the underlying encryption algorithm, and constructing an efficient lattice dual-mode encryption system will be an effective way to obtain the lattice UC secure OT protocol.
Disclosure of Invention
The invention aims to provide a dual-mode encryption method based on lattices, which can encrypt and transmit multi-bit plaintext messages on the basis of ensuring that the derived OT protocol has UC security.
The technical scheme adopted by the invention is that the lattice-based dual-mode encryption method is implemented according to the following steps:
step 1, generating a public reference string crs by using a Setup algorithm in a Messy mode or a Decryption mode;
step 2, selecting parameters, and Bob generates a public key pk by using a secret key generation algorithm0And the private key skb；
Step 3, Alice encrypts the multi-bit plaintext message by using an encryption algorithm and generates a ciphertext;
and 4, Bob decrypts the multi-bit plaintext message by using a decryption algorithm and recovers the plaintext message.
The present invention is also characterized in that,
in the step 1, the method specifically comprises the following steps:
in Messy mode: given n as input, let Setup algorithm output crs in Messy mode; n is a security parameter, crs is a common reference string, crs is (A, v), and matrix
Figure BDA0003126794950000031
Subject each element thereof to
Figure BDA0003126794950000032
Is uniformly distributed, column vectors are selected
Figure BDA0003126794950000033
Subject each element thereof to
Figure BDA0003126794950000034
Wherein q is the modulus,
Figure BDA0003126794950000035
an m x n order integer matrix expressed modulo q,
Figure BDA0003126794950000036
an m-dimensional integer column vector representing modulo q;
in Decryption mode: let Setup algorithm output crs in Decryption mode, given n as input, where matrix is (a, v)
Figure BDA0003126794950000041
Subject each element thereof to
Figure BDA0003126794950000042
Uniform distribution of the components;
Figure BDA0003126794950000043
subject each element thereof to
Figure BDA0003126794950000044
The distribution of the components is uniform, and the components are uniformly distributed,
Figure BDA0003126794950000045
n-dimensional integer column vector representing modulo q, selecting vector
Figure BDA0003126794950000046
Subject each element thereof to
Figure BDA0003126794950000047
The error distribution above, v-A s + e.
In the step 2, the method specifically comprises the following steps:
step 2.1, Bob generates a public key pk using the common reference string crs and the option b ∈ {0,1} as inputs to the key generation algorithm0And the private key skb(ii) a b is a channel decrypted by Bob, and when b is 0, a public key pk is generated0And the private key sk0Generating a public key pk when b is 10And the private key sk1；
Step 2.2, from
Figure BDA0003126794950000048
Each point on the top selected column vector s, sThe amount is subject to uniform distribution from
Figure BDA0003126794950000049
Each component on the upper selection vector e, e is obeyed
Figure BDA00031267949500000410
Error distribution over (c), selecting vector f e [ -B [ -c)2,B2]Wherein [ -B [ - ]2,B2]Is an integer interval, such that f is [ -B [ - ]2,B2]Uniformly distributing the upper layer;
step 2.3, let public key pk0As + e + f-b · v, private key skbS, pk is always satisfied for b e {0,1}b＝As+e+f，pk1-pk0＝v。
In step 3, the method specifically comprises the following steps:
step 3.1, from the message space {0,1}lSelecting a plaintext message mu ═ mu to be encryptedR,μ￡) Where l is the length of the message, mu is divided into two parts, where muRIs bit 1, mu￡Is the remaining l-1 bits;
step 3.2, selecting a branch b ', and encrypting Alice on a b' channel, and respectively calculating a public key pk for b 'belonging to {0,1}, wherein b' belongs to the group of {0,1}b'＝c:＝pk0+ b'. v, where c is for pkb'The symbol of (2).
When b' is 0, the public key pkb'＝0＝pk0+0·v＝pk0For encrypting messages mu-mu on 0 channel0(ii) a When b' is 1, the public key pkb'＝1＝pk0+1·v＝pk0+ v for encrypting messages mu-mu on channel 11；
Step 3.3, calculate the transpose P of the n-dimensional column vectori T＝ri TA, selecting a column vector
Figure BDA0003126794950000051
riEach component of (a) is distributed from Gaussian
Figure BDA0003126794950000052
Medium uniform selection, obeying discrete Gaussian distribution on set Z
Figure BDA0003126794950000053
Where r is a Gaussian parameter, i ∈ [ n ]]I.e. riAre independently decimated n times, where ri TIs riTranspose of (P)i TIs PiTransposing;
step 3.4, calculate the encryption μRThe latter 1 st bit cipher text
Figure BDA0003126794950000054
R is defined as a random rounding function satisfying the following form with the input being ZqThe output is a 1-bit value, where q is the modulus, ZqRing representing integer Z modulo q:
Figure BDA0003126794950000055
step 3.5, calculate the encryption mu￡The remaining l-1 bit cipher text
Figure BDA0003126794950000056
First of all, calculate
Figure BDA0003126794950000057
Wherein r iskFrom a plurality of independent riAny one of the vectors selected from the group consisting of,
Figure BDA0003126794950000058
is r ofkSetting a binary t-bit integer f ═ at-1…a1a0The value of the f residual bit is selected to be 0 or 1 except that the g +1 th bit is 0 and the g bit is 1, wherein
Figure BDA0003126794950000059
Setting generated key xi ═ (a)t-1,…,ag+2)ΤComputing the encryption of f
Figure BDA00031267949500000510
Step 3.6, get plaintext message μ ═ μR，μ￡) Is encrypted as
Figure BDA0003126794950000061
Step 3.7, set ciphertext to ct ═ ({ P)i,βi}i≤n,{k,σk,β￡})。
In step 4, the method specifically comprises the following steps:
step 4.1, recover μ of plaintext μRIn part
Figure BDA0003126794950000062
Due to the ciphertext of the 1 st bit
Figure BDA0003126794950000063
And because of R (P)i TS) and R (R)i TC) equal, and taking the bit value with larger number after decryption as the mu of the plaintext muRA moiety;
step 4.2, recover mu of plaintext mu￡In part
Figure BDA0003126794950000064
Calculating a secret key
Figure BDA0003126794950000065
Xi is set as
Figure BDA0003126794950000066
PkTo be from a plurality of PiAny one n-dimensional column vector selected from the above can be used to obtain mu of plaintext mu￡A moiety;
step 4.3, output plaintext message μ ═ μR,μ￡)。
The invention has the advantages that aiming at the defect that only a single-bit message can be encrypted in the grid dual-mode encryption method, a more efficient dual-mode encryption method is provided by utilizing the principle of a key reconciliation mechanism, the multi-bit message can be encrypted and transmitted on the basis of ensuring that the derived OT protocol can keep the safety of UC, the performance of the dual-mode encryption system is comprehensively improved, and certain innovation can be achieved on the bottom layer theoretical technical level.
Drawings
FIG. 1 is a flow chart of a lattice-based dual-mode encryption method of the present invention.
Detailed Description
The invention is described in detail below with reference to the drawings and the detailed description.
A Sender and a Receiver in an OT scene firstly inquire a reliable third party to obtain crs, and the Receiver is embedded into a self selection b to generate a public key pk0Sending to Sender, Sender receives public key and uses (pk) separately0,pk1) For two channel messages (mu)0,μ1) Encrypting to generate ciphertext (ct)0,ct1) Then sent to Receiver, which can only correctly decrypt ctbRecovery of mub。
The invention relates to a dual-mode encryption method based on lattices, which is shown in figure 1 and is implemented according to the following steps:
step 1, generating a public reference string crs by using a Setup algorithm in a Messy mode or a Decryption mode;
in Messy mode: given n as input, let Setup algorithm output crs in Messy mode; n is a safety parameter, crs is a common reference string, crs is equal to (A, v), and matrix
Figure BDA0003126794950000071
Subject each element thereof to
Figure BDA0003126794950000072
Is uniformly distributed, column vectors are selected
Figure BDA0003126794950000073
Subject each element thereof to
Figure BDA0003126794950000074
On the surface of the steel sheet is uniformA distribution, wherein q is the modulus,
Figure BDA0003126794950000075
an m x n order integer matrix expressed modulo q,
Figure BDA0003126794950000076
an m-dimensional integer column vector representing modulo q;
in Decryption mode: let Setup algorithm output crs in Decryption mode given n as input, where n is the security parameter, crs is the common reference string, let crs ═ a, v, where the matrix
Figure BDA0003126794950000077
Subject each element thereof to
Figure BDA0003126794950000078
Are uniformly distributed.
Figure BDA0003126794950000079
Subject each element thereof to
Figure BDA00031267949500000710
Wherein q is the modulus,
Figure BDA00031267949500000711
an m x n order integer matrix expressed modulo q,
Figure BDA00031267949500000712
n-dimensional integer column vector representing modulo q, selecting vector
Figure BDA00031267949500000713
Subject each element thereof to
Figure BDA00031267949500000714
Error distribution ofmFor error distribution, v ═ As + e ═ is calculated.
Crs generated in the Messy mode and crs generated in the Decryption mode are computationally indistinguishable. The Messy mode and the Decrypt mode are parallel, and only one of the two modes needs to generate the common reference string crs.
Step 2, selecting parameters, and Bob generates a public key pk by using a secret key generation algorithm0And the private key skbThe method specifically comprises the following steps:
step 2.1, Bob generates a public key pk using the common reference string crs and the option b ∈ {0,1} as inputs to the key generation algorithm0And the private key skb(ii) a b is a channel decrypted by Bob, and when b is 0, a public key pk is generated0And the private key sk0Generating a public key pk when b is 10And the private key sk1；
Step 2.2, from
Figure BDA0003126794950000081
Each component on the top-selected column vector s, s is subject to a uniform distribution, from
Figure BDA0003126794950000082
Obeying each component on the upper selection vector e, e
Figure BDA0003126794950000083
Error distribution over (c), selecting vector f e [ -B [ -c)2,B2]Wherein [ -B [ - ]2,B2]Is an integer interval, such that f is [ -B [ - ]2,B2]Uniformly distributing the upper layer;
step 2.3, let public key pk0As + e + f-b · v, private key skbAlways, pk is satisfied for b e {0,1}b＝As+e+f，pk1-pk0＝v。
And 3, utilizing an encryption algorithm by Alice to encrypt the multi-bit plaintext message and generate a ciphertext, specifically:
step 3.1, from message space {0,1}lSelecting a plaintext message mu ═ mu to be encryptedR,μ￡) Where l is the length of the message, mu is divided into two parts, where muRIs bit 1, mu￡Is the remaining l-1 bits;
step (ii) of3.2, selecting a branch b ', and encrypting Alice on a b' channel, and respectively calculating a public key pk for b 'belonging to {0,1}, wherein b' belongs to the public key pkb'＝c:＝pk0+ b'. v, where c is for pkb'The symbol of (2).
When b' is 0, the public key pkb'＝0＝pk0+0·v＝pk0For encrypting messages mu-mu on 0 channel0(ii) a When b' is 1, the public key pkb'＝1＝pk0+1·v＝pk0+ v for encrypting messages mu-mu on channel 11(ii) a For b ∈ {0,1, the public key pk is always satisfiedbAs + e + f corresponds to the message mu on the encrypted b channelb. The clear text message for either the 0 or 1 lane is applicable, and is denoted herein as μ.
Step 3.3, calculate the transpose P of the n-dimensional column vectori T＝ri TA, selecting a column vector
Figure BDA0003126794950000091
riEach component of (a) is distributed from gaussians
Figure BDA0003126794950000092
Medium uniform selection, obeying discrete Gaussian distribution on set Z
Figure BDA0003126794950000093
Where r is a Gaussian parameter where i ∈ [ n ]]I.e. riAre independently decimated n times, where ri TIs riTranspose of (P)i TIs PiTransposing;
step 3.4, calculate the encryption muRThe latter 1 st bit cipher text
Figure BDA0003126794950000094
Wherein c is calculated as (3b), R is defined as a random integer satisfying the following form, and the input is ZqThe output is a 1-bit value, where q is a modulus, ZqRing representing integer Z modulo q:
Figure BDA0003126794950000095
step 3.5, calculate the encryption mu￡The remaining l-1 bit cipher text
Figure BDA0003126794950000096
First, calculate
Figure BDA0003126794950000097
Wherein r iskFrom a plurality of independent riAny one of the vectors selected from the group consisting of,
Figure BDA0003126794950000098
is rkSetting a binary t-bit integer f ═ at-1…a1a0The value of the f residual bit is selected to be 0 or 1 except that the g +1 th bit is 0 and the g bit is 1, wherein
Figure BDA0003126794950000099
Setting generated key xi ═ at-1,…,ag+2)ΤComputing the encryption of f
Figure BDA00031267949500000910
Step 3.6, get plaintext message μ ═ (μ)R，μ￡) Is encrypted as
Figure BDA0003126794950000101
Step 3.7, set ciphertext to ct ═ ({ P)i,βi}i≤n,{k,σk,β￡})。
And 4, Bob decrypts the multi-bit plaintext message by using a decryption algorithm and recovers the plaintext message, and Bob can correctly decrypt the ciphertext message on the selected branch b channel and recover the plaintext mubThe recovered plaintext message mu cannot be correctly decrypted on the 1-b channel1-b(ii) a The method specifically comprises the following steps:
step 4.1, recover μ of plaintext μRIn part
Figure BDA0003126794950000102
Due to the ciphertext of the 1 st bit
Figure BDA0003126794950000103
And because of R (P)i TS) and R (R)i TC) equal, and taking the bit value with larger number after decryption as the mu of the plaintext muRA moiety;
step 4.2, recover mu of plaintext mu￡In part
Figure BDA0003126794950000104
Calculating a secret key
Figure BDA0003126794950000105
Xi is set as
Figure BDA0003126794950000106
PkTo be from a plurality of PiAny one of the selected n-dimensional column vectors,
Figure BDA0003126794950000107
is PkQ is modulus, where the probability of ξ being equal to ξ in step 3 is 1, μ in the clear text μ can be obtained￡A moiety;
step 4.3, output plaintext message μ ═ μR,μ￡)。
The method of the invention provides a more efficient dual-mode encryption method by utilizing the principle of a key reconciliation mechanism aiming at the defect that only a single-bit message can be encrypted in the dual-mode encryption method on the lattice, and can encrypt and transmit a multi-bit message on the basis of ensuring that the derived OT protocol can keep the safety of UC.

Claims (1)

1. A dual-mode lattice-based encryption method is characterized by being implemented according to the following steps:
step 1, generating a public reference string crs by using a Setup algorithm in a Messy mode or a Decryption mode; the method comprises the following specific steps:
in Messy mode: given n as input, let Setup algorithm output crs in Messy mode; n is a security parameter, crs is a common reference string, crs is (A, v), and matrix
Figure FDA0003649155820000011
Subject each element thereof to
Figure FDA0003649155820000012
Is uniformly distributed, column vectors are selected
Figure FDA0003649155820000013
Subject each element thereof to
Figure FDA0003649155820000014
Wherein q is the modulus,
Figure FDA0003649155820000015
an m x n order integer matrix expressed modulo q,
Figure FDA0003649155820000016
an m-dimensional integer column vector representing modulo q;
in Decryption mode: let Setup algorithm output crs in Decryption mode, given n as input, where matrix is (a, v)
Figure FDA0003649155820000017
Subject each element thereof to
Figure FDA0003649155820000018
Uniform distribution of the components;
Figure FDA0003649155820000019
subject each element thereof to
Figure FDA00036491558200000110
The distribution of the components is uniform, and the components are uniformly distributed,
Figure FDA00036491558200000111
n-dimensional integer column vector representing modulo q, selecting vector
Figure FDA00036491558200000112
Subject each element thereof to
Figure FDA00036491558200000113
The error distribution of (a), v ═ As + e;
step 2, selecting parameters, and Bob generates a public key pk by using a secret key generation algorithm0And the private key skb(ii) a The method specifically comprises the following steps:
step 2.1, Bob generates a public key pk using the common reference string crs and the option b ∈ {0,1} as inputs to the key generation algorithm0And the private key skb(ii) a b is a channel decrypted by Bob, and when b is 0, a public key pk is generated0And the private key sk0Generating a public key pk when b is 10And the private key sk1；
Step 2.2 from
Figure FDA00036491558200000114
Each component on the top-selected column vector s, s is subject to a uniform distribution, from
Figure FDA0003649155820000021
Obeying each component on the upper selection vector e, e
Figure FDA0003649155820000022
Error distribution over (c), selecting vector f e [ -B [ -c)2,B2]Wherein [ -B [ - ]2,B2]Is an integer interval, such that f is [ -B [ - ]2,B2]Uniformly distributing the upper layer;
step 2.3, let public key pk0As + e + f-b · v, private key skbAlways, pk is satisfied for b e {0,1}b＝As+e+f，pk1-pk0＝v；
Step 3, Alice encrypts the multi-bit plaintext message by using an encryption algorithm and generates a ciphertext; the method comprises the following specific steps:
step 3.1, from the message space {0,1}lSelecting a plaintext message mu ═ mu to be encryptedR,μ￡) Where l is the length of the message, mu is divided into two parts, where muRIs bit 1, mu￡Is the remaining l-1 bits;
step 3.2, selecting a branch b ', and encrypting Alice on a b' channel, and respectively calculating a public key pk for b 'belonging to {0,1}, wherein b' belongs to the group of {0,1}b'＝c:＝pk0+ b'. v, where c is for pkbThe symbol of';
when b' is 0, the public key pkb'＝0＝pk0+0·v＝pk0For encrypting messages mu-mu on 0 channel0(ii) a When b' is 1, the public key pkb'＝1＝pk0+1·v＝pk0+ v for encrypting messages mu-mu on channel 11；
Step 3.3, calculate the transpose of the n-dimensional column vector
Figure FDA0003649155820000027
Selecting a column vector
Figure FDA0003649155820000023
riEach component of (a) is distributed from Gaussian
Figure FDA0003649155820000024
Medium uniform selection, obeying discrete Gaussian distribution on set Z
Figure FDA0003649155820000025
Where r is a Gaussian parameter, i ∈ [ n ]]I.e. riAre independently extracted n times, wherein
Figure FDA0003649155820000028
Is r ofiThe transpose of (a) is performed,
Figure FDA0003649155820000029
is PiTransposing;
step 3.4, calculate the encryption μRThe latter 1 st bit cipher text
Figure FDA0003649155820000026
R is defined as a random rounding function satisfying the following form with the input being ZqThe output is a 1-bit value, where q is the modulus, ZqRing representing integer Z modulo q:
Figure FDA0003649155820000031
step 3.5, calculate the encryption mu￡The remaining l-1 bit cipher text
Figure FDA0003649155820000032
First of all, calculate
Figure FDA0003649155820000033
Wherein r iskFrom a plurality of independent riAny one of the vectors selected from the above-mentioned vectors,
Figure FDA0003649155820000034
is r ofkSetting a t-bit integer f ═ a in binary formt-1…a1a0The value of the f residual bit is selected to be 0 or 1 except that the g +1 th bit is 0 and the g bit is 1, wherein
Figure FDA0003649155820000035
Setting generated key xi ═ (a)t-1,…,ag+2)ΤComputing the encryption of f
Figure FDA0003649155820000036
Step 3.6, plaintext message
Figure FDA0003649155820000037
Is encrypted as
Figure FDA0003649155820000038
Step 3.7, set the ciphertext to
Figure FDA0003649155820000039
Step 4, Bob decrypts the multi-bit plaintext message by using a decryption algorithm and recovers the plaintext message; the method specifically comprises the following steps:
step 4.1, recover μ of plaintext μRIn part
Figure FDA00036491558200000310
Due to the ciphertext of the 1 st bit
Figure FDA00036491558200000311
And because of R (P)i TS) and
Figure FDA00036491558200000318
and taking the bit value with the maximum number after decryption as the mu of the plaintext muRA moiety;
step 4.2, recovery of the plaintext mu
Figure FDA00036491558200000312
In part
Figure FDA00036491558200000313
Calculating a secret key
Figure FDA00036491558200000314
Xi is set as
Figure FDA00036491558200000315
PkTo be from a plurality of PiAny one n-dimensional column vector selected from the above can be used to obtain the plaintext mu
Figure FDA00036491558200000316
A moiety;
step 4.3, outputting the plaintext message
Figure FDA00036491558200000317
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Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN110011782A (en) * 2019-03-11 2019-07-12 暨南大学 A kind of full homomorphic encryption algorithm of many-one
CN110519058A (en) * 2019-07-10 2019-11-29 中国科学院信息工程研究所 A kind of accelerated method for the public key encryption algorithm based on lattice

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US9281941B2 (en) * 2012-02-17 2016-03-08 International Business Machines Corporation Homomorphic evaluation including key switching, modulus switching, and dynamic noise management
US11070366B2 (en) * 2018-05-08 2021-07-20 Nec Corporation Dynamic anonymous password-authenticated key exchange (APAKE)
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CN111817853B (en) * 2019-09-24 2022-06-24 中国人民武装警察部队海警学院 Signcryption algorithm for post-quantum security
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Patent Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN110011782A (en) * 2019-03-11 2019-07-12 暨南大学 A kind of full homomorphic encryption algorithm of many-one
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